Odell's System of Shorthand
Odell's Short-Hand, as it was spelled at the time, is a version of Taylor shorthand.
It was published in 1830s-1850s, and went through multiple editions. According to contemporary authors (Heather W., Simple Shorthand, 1889), the manual "had a circulation of 289 000" copies.
You can read the manual on Google Books.
There is also an edition of the New Testament, written out in Odell's Shorthand, that can be used as a learning aide.